On non-deterministic supervisory control

Supervisory control theory (SCT) is examined in a non-deterministic setting. We show that language controllability of a supervisor is not necessarily equivalent to state controllability when the supervisor is non-deterministic. We give necessary and sufficient conditions for when equivalence holds. The input/output interpretation of the SCT is also examined in a non-deterministic setting. It is known that for a supervisor to act as a controller generating commands for the plant, the supervisor has to be inverse state controllable. We give sufficient conditions for when inverse state controllability is equivalent to inverse language controllability. In systems with concurrently competing production sequences, such as flexible manufacturing systems and multi-purpose batch plants, the specification typically becomes non-deterministic where several products compete for the same production resource. However, unless the plant is only partially observable, it is normally modeled as a deterministic discrete event process. We give necessary and sufficient conditions for the existence of a (possibly) non-deterministic supervisor in this special case.